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Daniel Semrau

Publications and source records attributed to Daniel Semrau.

18 recordsLinked to original sources
arXiv2024

Optimising O-to-U Band Transmission Using Fast ISRS Gaussian Noise Numerical Integral Model

We model the transmission of ultrawideband signals, including wavelength-dependent fibre parameters: dispersion, nonlinear coefficient and effective fibre core area. To that end, the inter-channel stimulated Raman scattering Gaussian noise integral model is extended to include these parameters. The integrals involved in this frequency-domain model are numerically solved in hyperbolic coordinates using a Riemann sum. The model implementation is designed to work on parallel GPUs and is optimised for fast computational time. The model is valid for Gaussian-distributed signals and is compared with the split-step Fourier method, for transmission over standard single-mode fibre (SSMF) in the O-band (wavelengths around the zero-dispersion wavelength), showing reasonable agreement. Further, we demonstrated SNR evaluation over an 80~km SSFM single-span transmission using 589x96 GBaud channels, corresponding to almost 59 THz optical bandwidth, fully populating the O, E, S, C, L and U bands (1260-1675 nm). The SNR evaluation is completed in just 3.6 seconds using four Nvidia V100 16GB PCIe GPUs. Finally, we used this model to find the optimum launch power profile for this system achieving 747 Tbps of potential throughput over 80 km fibre and demonstrating its suitability for UWB optimisation routines.

eess.SP↗
arXiv2020

Modelling the delayed nonlinear fiber response in coherent optical communications

Fiber nonlinearities, that lead to nonlinear signal interference (NLI), are typically regarded as an instantaneous material response with respect to the optical field. However, in addition to an instantaneous part, the nonlinear fiber response consists of a delayed contribution, referred to as the Raman response. The imaginary part of its Fourier transform, referred to as the Raman gain spectrum, leads to inter-channel stimulated Raman scattering (ISRS). ISRS is a nonlinear effect that redistributes optical power from high to lower frequencies during propagation. However, as the nonlinear fiber response is causal, the Raman spectrum obeys the Kramers-Kronig relations resulting in the real part of the complex valued Raman spectrum. While the impact of the imaginary part (i.e. ISRS) is well studied, the direct implications of its associated real part on the NLI are unexplored. In this work, a theory is proposed to analytically quantify the impact of the real Raman spectrum on the nonlinear interference power. Starting from a generalized Manakov equation, an extension of the ISRS Gaussian Noise (GN) model is derived to include the real Raman spectrum and, thus, to account for the complete nonlinear Raman response. Accurate integral expressions are derived and approximations in closed-form are proposed. Different formulations for the case of single -and dual polarized signals are derived and novel analytical approximations of the real Raman spectrum are proposed. Moreover, it is analytically shown that the real Raman spectrum scales the strength of the instantaneous nonlinear distortions depending on the frequency separation of the interacting frequencies. A simple functional form is derived to assess the scaling of the NLI strength. The proposed theory is validated by numerical simulations over C-and C+L band, using experimentally measured fiber data.

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arXiv2019

A Modulation Format Correction Formula for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

A closed-form formula is derived, which corrects for the modulation format dependence of the Gaussian Noise (GN) model in the presence of inter-channel stimulated Raman scattering (ISRS). The analytical result enables a rapid estimate of the nonlinear interference (NLI) for arbitrary modulation formats and avoids the need for complex integral evaluations and split-step simulations. It is shown that the modulation format dependent NLI can be approximated by two contributions, one originating from a single span and one asymptotic contribution for a large number of spans. The asymptotic contribution is solved in closed-form for an arbitrary link function, making the result applicable for generic fiber systems using lumped, distributed or hybrid amplification schemes. The methodology is applied to the ISRS GN model and a modulation format correction formula in closed-form is derived which accounts for an arbitrary number of spans, inter-channel stimulated Raman scattering, arbitrary launch power distributions and wavelength dependent dispersion and attenuation. The proposed formula is validated by numerical simulations over the entire C+L band for multiple fiber types.

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arXiv2018

A Closed-Form Approximation of the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

An accurate, closed-form expression evaluating the nonlinear interference (NLI) power in coherent optical transmission systems in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The analytical result enables a rapid estimate of the signal-to-noise ratio (SNR) and avoids the need for integral evaluations and split-step simulations. The formula also provides new insight into the underlying parameter dependence of ISRS on the NLI. The proposed result is applicable for dispersion unmanaged, ultra-wideband transmission systems that use optical bandwidths of up to 15 THz. The accuracy of the closed-form expression is compared to numerical integration of the ISRS Gaussian Noise model and split-step simulations in a point-to-point transmission, as well as in a mesh optical network scenario.

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arXiv2018

On the Impact of Fixed Point Hardware for Optical Fiber Nonlinearity Compensation Algorithms

Nonlinearity mitigation using digital signal processing has been shown to increase the achievable data rates of optical fiber transmission links. One especially effective technique is digital back propagation (DBP), an algorithm capable of simultaneously compensating for linear and nonlinear channel distortions. The most significant barrier to implementing this technique, however, is its high computational complexity. In recent years, there have been several proposed alternatives to DBP with reduced computational complexity, although such techniques have not demonstrated performance benefits commensurate with the complexity of implementation. In order to fully characterize the computational requirements of DBP, there is a need to model the algorithm behavior when constrained to the logic used in a digital coherent receiver. Such a model allows for the analysis of any signal recovery algorithm in terms of true hardware complexity which, crucially, includes the bit-depth of the multiplication operation. With a limited bit depth, there is quantization noise, introduced with each arithmetic operation, and it can no longer be assumed that the conventional DBP algorithm will outperform its low complexity alternatives. In this work, DBP and a single nonlinear step DBP implementation, the \textit{Enhanced Split Step Fourier} method (ESSFM), were compared with linear equalization using a generic software model of fixed point hardware. The requirements of bit depth and fast Fourier transform (FFT) size are discussed to examine the optimal operating regimes for these two schemes of digital nonlinearity compensation. For a 1000 km transmission system, it was found that (assuming an optimized FFT size), in terms of SNR, the ESSFM algorithm outperformed the conventional DBP for all hardware resolutions up to 13 bits.

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arXiv2017

The Gaussian Noise Model in the Presence of Inter-channel Stimulated Raman Scattering

A Gaussian noise (GN) model is presented that properly accounts for an arbitrary frequency dependent signal power profile along the link. This enables the evaluation of the impact of inter-channel stimulated Raman scattering (ISRS) on the optical Kerr nonlinearity. Additionally, the frequency dependent fiber attenuation can be taken into account and transmission systems that use hybrid amplification schemes can be modeled, where distributed Raman amplification is partly applied over the optical spectrum. To include the latter two cases, a set of coupled ordinary differential equations must be numerically solved in order to obtain the signal power profile yielding a semi-analytical model. However for lumped amplification and negligible variation in fiber attenuation, a less complex and fully analytical model is presented which is referred to as the ISRS GN model. The derived model is exact to first-order for Gaussian modulated signals and extensively validated by numerical split-step simulations. A maximum deviation of $0.1$~dB in nonlinear interference power between simulations and the ISRS GN model is found. The model is applied to a transmission system that occupies an optical bandwidth of $10$~THz, representing the entire C+L band. At optimum launch power, changes of up to $2$~dB in nonlinear interference power due to ISRS are reported. Furthermore, comparable models published in the literature are benchmarked against the ISRS GN model.

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arXiv2017

The Impact of Transceiver Noise on Digital Nonlinearity Compensation

The efficiency of digital nonlinearity compensation (NLC) is analyzed in the presence of noise arising from amplified spontaneous emission noise (ASE) as well as from a non-ideal transceiver subsystem. Its impact on signal-to-noise ratio (SNR) and reach increase is studied with particular emphasis on split NLC, where the digital back-propagation algorithm is divided between transmitter and receiver. An analytical model is presented to compute the SNR's for non-ideal transmission systems with arbitrary split NLC configurations. When signal-signal nonlinearities are compensated, the performance limitation arises from residual signal-noise interactions. These interactions consist of nonlinear beating between the signal and co-propagating ASE and transceiver noise. While transceiver noise-signal beating is usually dominant for short transmission distances, ASE noise-signal beating is dominant for larger transmission distances. It is shown that both regimes behave differently with respect to the optimal NLC split ratio and their respective reach gains. Additionally, simple formulas for the prediction of the optimal NLC split ratio and the reach increase in those two regimes are reported. It is found that split NLC offers negligible gain with respect to conventional digital back-propagation (DBP) for distances less than 1000 km using standard single-mode fibers and a transceiver (back-to-back) SNR of 26 dB, when transmitter and receiver inject the same amount of noise. However, when transmitter and receiver inject an unequal amount of noise, reach gains of 56% on top of DBP are achievable by properly tailoring the split NLC algorithm. The theoretical findings are confirmed by numerical simulations.

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arXiv2017

Achievable information rates estimates in optically-amplified transmission systems using nonlinearity compensation and probabilistic shaping

Achievable information rates (AIRs) of wideband optical communication systems using ~40 nm (~5 THz) EDFA and ~100 nm (~12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each individual channel have been evaluated for DP-64QAM, DP-256QAM, and DP-1024QAM modulation formats. The impact of full-field nonlinear compensation (FF-NLC) and probabilistically shaped constellations using a Maxwell-Boltzmann distribution were studied and compared to electronic dispersion compensation. It is found that a probabilistically shaped DP-1024QAM constellation combined with FF-NLC yields AIRs of ~75 Tbit/s for the EDFA scheme and ~223 Tbit/s for the Raman amplification scheme over 2000 km standard single mode fibre transmission.

cs.IT↗